Table REF  shows the compilation results of `PH' and the QAOA compiler [1]} on the 6 MaxCut problems.
We ran the QAOA compiler with 20 random seeds for each program and collected the averaged compilation results.
Comparing with the QAOA compiler, Paulihedral can achieve 31.2%, 16.3%, and 24.1% reduction in CNOT count, total gate count, and circuit depth, respectively on average, using only \(1.7\%\)  compilation time.
The overhead is about 50% in single-qubit gate count, but in QAOA the CNOT count is usually over \(3-4\times \)  higher than single-qubit gate count and CNOT error rate is usually 10\(\times \)  higher on the SC backend.
Therefore, `PH' significantly outperforms QAOA compiler, even though it is more general purpose and not tailored to a single algorithm.
This is because `PH' employs a block-wise optimization for searching SWAPs and the search scope is much larger than that of the QAOA compiler's greedy search.
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